If $u= \sin ^{-1} \bigg( \large\frac{x^2+y^2}{x+y}\bigg)$ then $x \large\frac{\partial u}{\partial x}$$+ y \large\frac{\partial u}{\partial y}$ is equal to :

Question

$$\begin {array} {1 1} (a)\;\sin u & \quad (b)\;\tan u \\ (c)\;\cos u & \quad (d)\;\cot u \end {array}$$